Insight into the corrosion mitigation performance of three novel benzimidazole derivatives of amino acids for carbon steel (X56) in 1 M HCl solution

Three new organic molecules having a benzimidazole base were synthesized and used for the protection of carbon steel (X56) against corrosion in 1.00 M HCl solution. The protection against corrosion was assessed by electrochemical frequency modulation (EFM), electrochemical impedance spectroscopy (EIS) and potentiodynamic polarization (PDP). In addition, the electronic and molecular structure of the synthesized molecules were computationally investigated and correlated to corrosion inhibition. Global reactivity descriptors, molecular orbitals (FMO and NBO) and local reactivity descriptors (molecular electrostatic potential map and Fukui functions) were discussed. The results showed a maximum protective efficiency range between 95% and 98% indicating high corrosion inhibition. Moreover, all molecules were able to combat the cathodic as well as anodic reaction simultaneously, revealing a mixed-type resistance. SEM and EDX verified effective adhering film formation to the metal surface. In accordance, the theoretical calculations showed effective electron reallocation from the organic film to the X56 c-steel surface. Furthermore, the adsorption annealing calculations revealed that structural layers of these molecules hold parallel and close to the metal surface with adsorption energy from 249.383 to 380.794 kcal mol−1, showing strong inhibitor-metal contact.


Introduction
Due to increased demand for useful fuels, upgrading heavy hydrocarbons to light fuels like diesel and gasoline has become more popular. 1 The most difficult problem in the petroleum rening industry is producing high-quality fuels. 2,3 Carbon steel pipelines, tanks, and the renery's infrastructure that carry crude oil 4-6 suffer from corrosion, which is a serious issue in the oil and gas industry, and it frequently results in equipment failure and distortion. 7,8 Corrosion can occur when metals interact with crude oil elements like sulphur and naphthenic organic acids such as naphthalene and naphthene acids. [9][10][11] Oil well acidication can also results in corrosion. 12,13 Further research is needed to understand how these materials respond to corrosive conditions. 14 Carbon steel (CS) has been included in considerable use in various situations in the petroleum industry. 15 Among the most corrosive media, acid solutions, in water, are commonly employed in industry for pickling and acid cleaning of boilers and oil wells. [16][17][18] Carbon-corrosion steel's resistance is signicantly lower than other metals in acidic conditions 19 and raised using a variety of approaches 20,21 in which organic inhibitors were commonly used. 22 The hydrochloric acid solution is commonly used in industrial applications such as cleaning, pickling, and galvanizing metals and it is also an important component of several industrial processes such as descaling, rening, and preparation. [23][24][25] HCl is typically used at a concentration of 5-10% for this purpose, which results in a high rate of corrosive pitting and damage to the surface of steel construction components. 4,26,27 Corrosion inhibitors are typically added to the acid wash solution to prevent corrosion. 28,29 Almost all corrosion inhibitors are prepared from organic compounds with heteroatoms in their aromatic or cyclic structures. 30 These compounds have a lot of heteroatoms (like N, S, P, and O) and many bonds, which makes it easier for the inhibitor to stick to the surface of the metal. 31,32 Some quantum mechanical investigations have successfully related corrosion prevention efficacy and the molecular characteristics of certain organic molecules. [33][34][35][36] Despite the huge number of organic compounds available, selecting an effective corrosion inhibitor for a specic system is limited by the specicity of the inhibitors and the wide range of corrosion systems. 19,20,[37][38][39] Scientists are still looking for corrosion inhibitors that are less expensive, non-toxic, and safe for both the environment and personnel. In furtherance of the search, the present work focuses on the synthesis of three novel water-soluble aminoacids benzimidazole derivatives (1-amino-1-(1H-bezo [d] imidazole-2-yl-2-ol, B1), 1-(1H-bezo[d]imidazole-2-yl)-3methylbutan-1-amine, B2, and1-(1H-benzo[d]imidazole-2-yl)-3-(methylthio) propan-1-amine, B3) and investigation of their inhibition effect on the corrosion of carbon steel (Grade X56) in 1 M HCl solution using electrochemical methods in addition to SEM/EDX/mapping spectra studies. Moreover, a quantum chemical approach was used to relate the electronic properties of the synthesized molecules to the inhibitory effect on carbon steel.

Chemical materials and instrumentation
The threonine, leucine, and methionine amino acids and orthophenylenediamine employed in the present research are of analytical grade and were purchased from Sigma Aldrich; they were not further puried. Toluene solvent and hydrochloric acid were purchased from the Scharlau Company. Using matching silica cells and a Shimadzu UV-1800 spectrophotometer, the electronic spectra of the compounds were measured in an ethanol + water mixture (2 : 8). The KBr discs were used to record the infrared (IR) spectra of metal chelates across the range of 400 to 4000 cm −1 using a Fourier transforms infrared (FTIR) spectrophotometer (Shimadzu FTIR-8400S). Using D 2 O as a solvent, a Bruker DPX-300 spectrometer was used to record 1 H and 13 C NMR spectra with broadband decoupling of 1 H at 600 MHz and 150 MHz. The compounds' elemental analyses (C, H, and N) were performed using the Flash EA 112 Elemental Analyzer. The percentage of the sample's constituents was determined using spectroscopy via emission and foundrymaster Xpert instrument. Aer immersion in 1 M HCl solution with and without B1, B2, and B3 compounds, the surface morphology of carbon steel (Grade X56) coupons was analyzed using a eld emission scanning electron microscope (FESEM) (ZEISS Sigma), energy-dispersive X-ray (EDX) spectroscopy, and mapping images.

Synthesis of benzimidazole derivatives
O-phenylenediamine (5.0 mmol) was added to a round-bottom ask containing 10 mL of toluene and stirred for 40 seconds to ensure even miscibility. This solution was added dropwise to equimolar solutions of amino acids (threonine, leucine, and methionine, 5.0 mmol), and the color of the solution slightly changed. The mixture was heated under reux for nine hours at a carefully controlled temperature of 85-95°C. 40 The solution Scheme 1 Synthetic route of the studied three amino acids derivatives. was cooled and allowed to stand overnight to afford a colored solid, ltered by suction and oven-dried to afford the crystalline solid of the expected products B1, B2, and B3, as represented in Scheme 1. Thin-layer chromatography (TLC) was used to monitor the completion of the reaction.

Corrosion inhibition approach
The initial samples of carbon steel (Grade X56) were obtained from pipes transporting oil in southern Iraq. The required samples were then prepared in order to create the study's working electrodes. The element percentage of carbon steel alloy was determined utilizing emission manner at temperature of 24°C and a humidity percentage of 32%. It was found to have the following percentages (wt%): carbon (0.174), manganese (1.36), silicon (0.367), sulfur (0.0035), phosphor (0.0116), nickel (0.0333), copper (0.0339), vanadium (0.0039), chromium (0.012), molybdenum (less than 0.002), and iron (balance). To prepare the working electrode, the mechanical method was used to cut the carbon steel into specimens of 1.5 cm × 1.5 cm × 1 cm dimensions. Aer that, they were encased in an epoxy resin, and the exposed area of 1 cm 2 was abraded by hand using an angle grinder. This was done to remove any excess epoxy resin and then various grades of emery paper (600-1200) were used to remove rust and scale. Before the samples were used, the surface of each one was meticulously cleaned with distilled water, degreased with acetone and hot benzene, and then airdried at room temperature. The potentiostat/galvanostat device was used for the electrochemical tests at 298.15 K. The Echem analyst program was used to gather and analyze the data. The carbon steel (Grade X56) was the working electrode in the electrochemical setup. The saturated calomel electrode (SCE) was the reference electrode while the platinum foil was the counter electrode. All three electrodes were immersed in the 1 M HCl solution. Prior to the experiments, the carbon steel sample was allowed to corrode naturally without any external current or potential for 1800 s to produce a stable open-circuit potential (OCP). The studies were conducted with and without B1, B2, and B3 inhibitors. Carbon steel samples were tested for electrochemical potentials using the PDP technique with the potential ranges from 0.4 to +0.6 at a scan rate of 0.2 mV s −1 . The corrosion potential (E corr ), cathodic and anodic Tafel slopes (b c and b a ), corrosion current density (i corr ), and corrosion rate (k) were all extrapolated from Tafel plots. Using eqn (1) and (2) we can determine the inhibition efficiency (h p (%)) 41,42 and corrosion rate. 43 As, k is a conversion factor, i corr is the corrosion current density, EW is the equivalent weight, and d is the density. The corrosion current densities in the absence and presence of different inhibitor concentrations are denoted by i 0 corr and i corr , respectively. The impedance measurements were performed in the frequency response spectrum range of 1 Hz to 100 kHz at amplitude of ±10 mV. An equivalent circuit was utilized for tting impedance spectrum data. Estimating parameters such as the charge transfer resistanceR ct , solution resistanceR s , and inhibition efficiency (h z (%)) is essential. The impedance spectrum was represented using Nyquist and Bode plots. The corrosion inhibition efficiency, denoted by h z (%), was determined by applying the following eqn (3) to the data: 44,45 h z ð%Þ ¼ 100 where R ct and R 0 ct represents the charge transfer resistances in the presence and absence of the studied inhibitor. In addition, electrochemical noise (EN) tests were performed. Two carbon steel samples were employed as working electrodes while a saturated calomel electrode (SCE) was used as a reference electrode. The electrochemical cell was placed in a Faraday cage to eliminate electrical interference. The exposed surface area of each working electrode was 1 cm 2 and the distance between them was approximately 1 cm. The electrochemical current noise was measured using a galvanic coupling current between two working electrodes. The electrochemical potential noise was measured under free corrosion conditions between the reference electrode and two connected working electrodes. Current and potential noises were recorded for 720 seconds at a frequency of 5 Hz and a repeat time of 15 seconds. A low-pass lter with a frequency of 2.5 Hz was utilized to reduce frequencies over the Nyquist frequency during data recording. The following eqn (4); 46 was used to derive the inhibitory performance values from the EN measurements: where h N the percentage of inhibition efficiency, R −0 rms is the average noise resistance in an inhibitor-free medium, and R −inh rms is the average noise resistance in an inhibitor-containing medium. In addition, the EFM criteria were satised by employing a potential perturbation signal (10 mV amplitude) with two sine waves at 2 and 5 Hz and 16 cycles. The selection of these frequencies was based on three justications. The more prominent peaks were used to determine the corrosion current density (i corr ), the Tafel slopes (b c and b a ) and the causality factors (CF-2 and CF-3). Eqn (5); 47,48 can be used to determine efficiency as a function of current density.
Electrochemical experiments were duplicated at each concentration of the tested inhibitors to ensure the experimental data's accuracy.

Computational investigation
Initial guesses of B1, B2 and B3 molecules were prepared by ChemBioDraw Ultra 14.0 in 2D dimensions then a minimization (energy/geometry) was performed by Gaussian 09 revision-A.02-SMP package 49 at RHF/6-31g level. The optimized parameters were reached aer 23 iterations by achieving the convergence criteria indicated by Gaussian 09: the maximum remaining force on an atom and the average (RMS, root mean square) force on all atoms are below the tolerance threshold 45 × 10 −5 and 30 × 10 −5 Hartrees, respectively as well as the maximum structural dri of one coordinate and RMS change over all structural parameters in the last two iterations are below 18 × 10 −4 and 12 × 10 −4 Å, respectively. It is worthy to mention that the maximum force and RMS force were two orders of magnitude smaller than the indicated thresholds (i.e.: 38 × 10 −6 and 7 × 10 −6 Hartrees, respectively) which reveal that a stationary point is reached regardless of the obtained values of the displacements. The obtained optimized parameters were used to re-optimize the structures by Density Functional Theory at B3LYP/6-31g(d,p) level of theory 50-52 as well as carrying out Hirshfeld population analysis. Similar convergence criteria to that of RHF calculations were obtained aer 42 iterations though. Obtained molecules representing local minima were sketched by Gaussview 6. 53 Oen DFT calculations underestimate Frontier molecular orbitals eigenvalues, therefore the DFT calculations were repeated using TD-DFT method to calculate the lowest excited state energy and therefore correct the value of DE gap between HOMO and LUMO. Six energy states were included for this calculation at TD-B3LYP/6-31g(d,p) following the procedure described by ref. 54. E HOMO and E LUMO as well as their corresponding reactivity descriptors were obtained as described by ref. 54. HOMO and LUMO surfaces with isovalue of 0.02 and density of 0.0004 were presented using the molecular orbital editor of Gauss view 6. 53 Natural bond orbitals (NBOs) were calculated at B3LYP/6-31g(d,p) level and presented for selected sites of B1, B2 and B3 molecules. NBOs surfaces were obtained using the NBO Version 3.1 (ref. 55) in Gaussian 09 soware and plotted using the same isovalue of 0.02 and density of 0.0004 in order to compare them to FMOs. In addition, Fukui functions were calculated by adding a positive and a negative charge to the neutral molecules and then re-optimizing it at B3LYP/6- 31g(d,p). The calculated condensed Fukui functions f k + and f k − were extracted. A full view of the corrosion system (steel/corrosive medium/ inhibitor) was considered using the adsorption locator tool in materials studio soware. 56 Fig. 4. An absorption band was observed between 228 and 267 nm which could be associated with a p-p* transition originating primarily in the azomethine chromophore and the n-p* transition electronic for the imidazole aromatic ring in 488 nm for the B1 structure. The results for B2 showed bands at 230 nm and 280 nm, both assigned to p-p* transitions. The band at 498 nm was assigned to n-p* transitions. The results for B3 were a strong band at 229 nm and a weak band at 272 nm. Both bands were attributed to p-p* transitions. The n-p* transitions in the imidazole aromatic ring were related to the band at 490 nm. When compared to the p-p* transition that observed in the two electronic bands, the absorption bands assigned to the n-p* transition have different values for the three compounds, which are related to the nature of the chromophore that responded to the kind of transition with respect to the nature of the solvent that was used.

Electrochemical measurements
3.2.1. PDP measurements. Potentiodynamic polarization (PDP) was used to determine how fast the cathodic and anodic reactions were on the carbon steel surface. Based on the answer, it can be gured out how the inhibitors (B1, B2, and B3) affect the corrosion reaction of carbon steel in an aerated 1.0 M HCl solution at 30°C. Fig. 5 depicts the curve of potentiodynamic polarization measurements (Tafel plots) for uninhibited and inhibited (with various concentrations) carbon steel corrosion. The main point noticed from the gure is that the addition of B1, B2 and B3 causes a displacement of both curves (anodic and cathodic) towards the lower side of i corr when compared to the blank curve, which reveals towards the reduction in the corrosion reactions. Table 1 displays the inhibition efficiency and corrosion reaction data (corrosion potential (E corr ), corrosion current density (i corr ), anodic Tafel slope (b a ), and cathodic Tafel slope (b c )) obtained by extrapolating the linear region of the polarization plot. Table 1 demonstrates that when B1, B2, and B3 inhibitors were added, the corrosion current density (i corr ) values dropped dramatically compared to the uninhibited solution. Furthermore, as the inhibitor concentration increases, the i corr values decrease and the inhibition efficiency (h p (%)) increases. 57 B3 seems to be a better inhibitor than B1 and B2. This means that it is more likely to slow down the anodic and cathodic reactions on carbon steel under the conditions of the experiment. This means that B3 is an efficient corrosion inhibitor. As  the inhibitor is introduced, the molecules adsorb on the metal surface and obstruct the active sites. The highest h p (%) of B3 is attained at the highest inhibitor concentration because the active sites are inhibited more severely at the higher inhibitor concentration which is 10 mM in this case. Fig. 5 shows that when B1, B2, and B3 inhibitors were present, both the anodic and cathodic currents were slowed down. This is because the Tafel regions in the polarization curves of the solution under study were well delineated, and the inhibiting action of these inhibitors on both cathodic and anodic processes is approximately the same. For that, the inhibitor may decrease the corrosion rate through the reduction of carbon steel reactivity and a decrease in the anodic reaction, cathodic reaction, or both that arise from the adsorption of the inhibitor on the carbon steel surface. The difference between E corr values measured in the absence and presence of B1, B2, and B3 compounds is less than 85 mV, as shown in Table 1. As a result, these compounds block both the cathodic (hydrogen evolution) and anodic (metal dissolution) processes, acting as a mixed-type inhibitor. 58 The slopes of the anodic (b a ) and cathodic (b c ) Tafel lines are slightly altered with the variety of inhibitor concentrations. This implies that the molecules B1, B2, and B3 inuence the mechanism of carbon steel dissolution, and the i corr values calculated from both the cathodic and anodic curves decreased by forming a protective layer against acid attack. 3.2.2. EFM measurements. EFM is well known as a quick and effective non-destructive corrosion rate assessment method. 59 Without prior knowledge of Tafel constants, the EFM approach instantly yields corrosion current values. 60 The intensity of the two higher peaks in the intermodulation spectra show the link between current density (i) and frequency in respect to the selected two applied excitation frequencies of 2 and 5 Hz. 61 The EFM-intermodulation spectra of (X56 c-steel/ 1.00 M HCl/B3) at 30°C are gathered in Fig. 6. In addition, the extracted electrochemical kinetic parameters are recorded in Table 2. The consistency between perturbation and response signals is indicated by the CF2 and CF3 values which are close to their ideal values of 2 and 3. 62 Fig. 6 depicts the sequentially suppressed spectra associated with the decrease in i corr while B3 concentration increases. The corrosion rate dramatically decreased from 1211.0 mpy to 59.49 mpy, 38.07 mpy and 12.47 mpy by the addition of 10 mM of B1, B2 and B3, respectively. Also, a slight change in Tafel slopes values (b c and b a ) is noticed by the addition of B1, B2 and B3 compounds in agreement with data from PDP measurements. With the addition of 10 mM of B3, i corr values dropped precipitously from 1077 mA cm −2 (blank) to 43.99 mA cm −2 , producing protection efficiency of 95.92%. A similar behavior is observed for B2 and B1 inhibited c-steel specimens: i corr decreased to 57.77 mA cm −2 and 85.02 mA cm −2 with a maximum efficiency of 94.64% and 92.11% respectively. The signicant decrease of i corr values articulates the creation of an organic adsorption layer at the X56 c-steel/ 1.00 M HCl interface by the order B3 > B2 > B1.
3.2.3. EN measurements. The relationship between time and electrochemical noise (current and voltage), for the blank and B3 molecule at ve different concentrations (1, 3, 5, 7 and 10 mM), is shown in Fig. 7. The extracted parameters for EN data are collected in Table 3. It is apparent that the 1 M HCl blank solution has more positive voltage and current areas with uctuating potential and noise than the solution with B3 added. For the blank solution, the potential and current noise was stabilized at 6.02 mV and 8.981 fA, respectively. Due to their poor noise resistance, the H + and Cl − ions enhance the values of potential and current noise on the X56 c-steel surface. They have the ability to corrode X56 c-steel surfaces, and during EN tests, H 2(g) is seen on the X56 c-steel surfaces. On the other hand, the B1, B2 and B3 compounds cause the electrochemical noise uctuation to move to more negative areas. This indicates that the B1, B2 and B3 compounds signicantly reduces the corrosion current and potential. 63 The change in voltage and current depends on B1, B2 and B3 concentrations. For example, in presence of B3 compound, the potential stabilizes at 30.15 mV at 1 mM, 37.11 mV at 3 mM, 45.80 mV at 5 mM, 94.59 mV at 7 mM and 74.62 mV at 10 mM. The inhibitors efficiencies were estimated as a function of resistance The value of R rms in the blank solution was 0.671 GU and enhanced by the successive addition of B1, B2 and B3 compounds. For example, in presence of B3 compound, R rms values were 4.093 GU at 1 mM, 5.100 GU at 3 mM, 6.354 GU at 5 mM, 8.408 GU at 7 mM and 10.065 GU at 10 mM. At 10 mM and the efficiency approached 91.25% for B1, 92.55% for B2 and 93.34% for B3. The highest value of electrical charges (q) transferred between anode and cathode was related to the blank solution (6.294 pC) as a result of high corrosion rate. 64 While in presence of B1, B2 or B3, its value reduced by blocking the active sites for electrical charges transfer leads to more corrosion resistance.
3.2.4. EIS measurements. Fig. 8 displayed Nyquist plots and the equivalent circuit for X56 c-steel surface in 1.0 M HCl solution containing B1, B2 and B3 molecules at 30°C. The related Bode and phase angle plots are collected in Fig. 9. In Nyquist diagrams, there is just one depressed semi-circle (related to one time constant) which symbolizes chargetransfer controlled corrosion pathway. 65 Due to the irregularity and roughness of the adsorbed constituent and X56 c-steel surface, Nyquist plots do not depict perfect semicircles. 66 The presence of the B1, B3 and B3 compounds leads to increase of the semi-circle diameter as a function of concentration with priority of B3 over B2 and B1. The impedance data was tted to a suitable equivalent circuit (R s (CPE R ct )) and the extracted data The values of Y 0 and C dl in the blank solution were high (492.40 mU −1 s n cm −2 and 298.745 mF cm −2 ) and decreased by the presence of B1, B2 and B3 compounds. As C dl is inversely related to the double layer thickness, so the depression in C dl values is associated with increasing the double layer thickness by replacing the adsorbed water, H + and Cl − chemical species with the organic B1, B2 and B3 molecules. 69 The other proof of the adsorbed lm of B1, B2 and B3 molecules on the X56 c-steel surface is the close values of n to unity in the presence of B1, B2 and B3 molecules.
The Bode plots (Fig. 9) consist of one phase that belongs to one time constant. Generally, higher corrosion resistance is associated with a bigger capacitive loop at jZj 0.01Hz . Moreover, a stronger corrosion barrier layer was shown by the greater and broader phase angle in the middle frequency band. 70 The value of jZj 0.01Hz in the blank solution was the lowest and enhanced by the gradual addition of B1, B2 and B3 compounds to achieve almost 2 orders of magnitude greater than that of the blank, demonstrating good X56 c-steel protection. The phase angles are almost zero at high frequency conrming that the electrolyte exhibiting a low resistance as indicated by the equivalent circuit with the solution resistance (R s ) and the beginning of the adsorption process. On the other hand, the increase in the phase angles at the low-frequency regions conrms the better corrosion inhibition with B1, B2 and B3 indicating that the inhibitors molecules get adsorbed on the surface of steel and forming a protective lm. 71 Furthermore, when B1, B2 and B3 molecules present, the phase angle expands (towards −90), demonstrating their inhibitory impact on X56 c-steel. 72 The phase angle for the blank is −52.31 and at 10 mM; it was shied to −73.13 (B1), −73.07 (B2) and −74.32 (B3). The Bodes lines slopes at the middle frequency range shi to −1 in presence of B1, B2 or B3 compounds as indication of enhanced capacitance behavior. The relaxation time (s) was calculated as the product of R ct × C dl , 73 and listed in Table 4. The addition of the investigated molecules increased the values of s from 7.206 mS to 31.064 mS (B1), 47.867 mS (B2) and 56.405 mS (B3), which may be explained on the basis that building up dense layers of B1, B2

Adsorption considerations
The interaction of B1, B2 and B3 molecules with X56 c-steel surface could be physical or chemical forming single layer or multiple layers. The data from EFM were subjected to several adsorption isotherms to select the most suitable one. The graphical representations of six adsorption models were collected in Fig. 10 and the extracted tting parameters were collected in Table 5. Based on R 2 values (R 2 z 1), 75    DG ads values ranged from −28.14 kJ mol −1 to −31.14 kJ mol −1 as indication of spontaneous collaborative mode of physical and chemical adsorption (−20 kJ mol −1 physisorption > collaborative or mixed mode > −40 kJ mol −1 chemisorption). 79

FESEM analysis
The surface morphology of carbon steel samples immersed for 24 hours in 1.0 M HCl with and without B1, B2, and B3 inhibitors was analyzed using FESEM. As shown in Fig. 11a, the surface of the carbon steel was polished before it was immersed in a corrosive acidic solution. Inevitably, removing corrosion with a succession of silica carbide sheets will leave visible scratches on the surface of the carbon steel. These scratches cannot be prevented. Fig. 11b shows a blank FESEM micrograph of the metal-carbon surface immersed in an acidic solution of 1.0 M HCl. In absence of an inhibitor, metal corrosion would cause much damage to the surface of the specimen. It is clear to see many pits of different sizes and depths all over the carbon steel surface exposed to an acidic corrosive. This shows that the corrosion process has made much damage. The surface became rough because of dissolution in the corrosive media. Furthermore, a thick porous layer of corrosion products like oxide lms covered all surface metal, and the surface was strongly damaged. 80 The damage on the specimen surface was signicantly reduced aer the addition of B1, B2, and B3 corrosion inhibitors (10 mM) to the corrosive solution, as shown in Fig. 12a-c, because the pits and cracks were not as aggressive as the previous ones, as shown in Fig. 11b. The image of FESEM for carbon steel in 1.0 M HCl with 10 mM B3 shows that some parts had smoother surfaces and fewer cracks. However, in case of B1 inhibitor, the carbon steel's protective layer seems cracked while B2 inhibitor can be uniform and stick to the surface metal. It was conrmed that the B1, B2, and B3 inhibitors work well as inhibitors because they can form a protective layer by adsorption that can protect the metal surface from a corrosive environment. Thus, the presence of B1, B2, and B3 compounds can enhance the surface morphology of carbon steel. They are effective corrosion inhibitors by decreasing the interaction between the metal surface and the corrosive solution.
We performed an EDX analysis to support these results further. EDX analysis reveals the semi-quantitative distribution of elements on the surface of carbon steel. The ndings are presented in Fig. 12 and Table 6. Aer 24 hours in 1.0 M HCl with 10 mM of inhibitors, the elemental distribution on the surface of the carbon steel was analyzed by EDX (Fig. 12). Surface elemental composition aer 24 hours in 1 M HCl displayed another peak, indicative of sulphur (S) element, as shown in Fig. 12c. The EDX spectra of B1 revealed a small amount of N by weight, but the 12.8% O composition was easily discernible (Table 6). EDX mapping images show the relative abundance of O and N elements. The corrosion reaction was slowed because of the presence of N, O, and S atoms, which served as active centers for adsorption and lm formation on the metal surface according to the structure of inhibitors.

Molecular reactivity
3.5.1. Global reactivity. The electrons lost by metals in a corrosion reaction can be compensated by adsorption of organic inhibitors on the metal surface so that the reaction can be controlled. The adsorption should guarantee an ease electron ow from the inhibitor to the metal surface. Molecules with low band gap, low ionization potential and low chemical hardness are the best candidates for such effective adsorption. 81 Although the band gap can be calculated directly by subtracting the eigenvalue of HOMO from that of LUMO, common DFT methods don't predict both HOMO and LUMO eigenvalues correctly resulting in an inaccurate band gap. Following the procedure suggested by Zhang and Musgrave et al. 54 an accurate band gap can be obtained using time dependent (TD) calculations.
A correction to HOMO can be calculated from the following relation: Fig. 10 The different adsorption models for B1, B2 and B3 compounds on the steel surface in 1.0 M HCl using data obtained from EFM measurements at 30°C.
A correction to LUMO can be calculated from the following relation: The calculated eigenvalues of both HOMO and LUMO are presented in Table 7 along with the corresponding global reactivity indices while their densities are plotted in Fig. 13. The estimated DE gap calculated according to Zhang and Musgrave et al. 54 procedure for B1, B2 and B3 molecules are 5.27, 5.29 and Table 5 Adsorption isotherms models of the inhibitors with values of R 2 , slopes, intercepts, K ads , and DG ads obtained by using data from electrochemical measurements a      molecules are very close in size and shape reecting the proximity of molecular structure of these molecules and hence accounting for the obtained close inhibition efficiencies to the corrosion of mild steel in HCl solution. Moreover, synthesized molecules with low chemical hardness (1.94 ± 1; Table 7), are good adsorbates forming stable lms on the adsorbent which is the metal in this case. In addition, the electron ow from inhibitor to the metal can be estimated using the following function as suggested by Pearson: 82 where c and h are electronegativity and chemical hardness, respectively. The estimated DN for the B1, B2 and B3 molecules are 0.102, 0.075 and 0.041, respectively (Table 7) showing good ow of electrons from these molecules to the mild steel surface. Overall, calculated reactivity parameters reveal an ease and effortlessness electron share from the synthesized molecules to the metal surface which explains the highly obtained electrochemical inhibition efficiencies. 3.5.2. Natural bond orbital analysis. Table 8 lists NBOs of the orbitals of B1, B2 and B3 molecules from HOMO to HOMO-7 which are the expected sites of interaction with metal surface. The list includes the type of orbital, its population, energy, NBO and hybridization limited to s and p characters. Furthermore, the orbital densities are sketched and included in Fig. 14 by the same order. NBOs order suggest that the orbital with higher energy (i.e. HOMO) should has the highest donating probability to the metal. Therefore, it resolves the HOMO of the FMOs into individual bond by bond orbital ordered according to their donating priority. Accordingly, the electron ow from the inhibitor B1 to the metal is as follows: BD (2) C 10 -C 11 > BD (2) C 7 -C 8 > BD (2) C 12 -C 13  Fig. 14 shows the origin of these bonding orbitals; for example, bonding orbital BD (2) C 10 -C 11 belongs to the HOMO of B1 molecule. In other words, the HOMO of B1 molecule is localized on the double bond C 10 -C 11 of the benzimidazole ring. In this order, the second lone pair of oxygen atom of the hydroxyl group comes late at HOMO−7 which indicates weaker ability to reallocate its density into empty orbitals of the metal. Similarly, the electron ow from inhibitor B2 has the following order (Table 8 It is noticeable that B2 has the same donating sites with the same order as molecule B1 except that B2 doesn't have Oxygen atom. NBOs of B3 molecule reveal similar electron ow character as well (Table 8 3.5.3. Local reactivity. While global reactivity descriptors relate the reactivity to the orbitals belongings, local reactivity concerns the sites (atoms, functional groups, and electrostatic surfaces) where the molecule can donate or accept electrons. A good inhibitor should have atoms or sites that are rich in electrons. A one way to explore these sites is the investigation of the molecular electrostatic potential (MEP) map (Fig. 15). In MEP, the sites with low electrostatic potential are rich in  electrons while sites with high electrostatic potential are poor in electrons. 83 The rst one is characterized by red color and the latter by blue color while sites with green color points to intermediate potential. Fig. 15 show that the color content follows the order: green > red > blue. While widespread green sites are common in organic molecules, MEP maps of B1, B2 and B3 molecules are depicted with electron rich sites much more than electron poor ones though. The red regions are localized on the benzimidazole part of the molecule which agrees with that HOMO is localized on both phenyl and imidazole rings and agrees also with that NBOs suggests that benzimidazole part has the priority to contact metal surface. Although MEP map labels the donating sites within the molecule, the magnitude of this donation can't be assessed from MEP map. Instead, Fukui functions as a powerful tool to estimate the nucleophilic and electrophilic tendency of a particular atom. To do so, the molecule is positively and negatively charged so that the second derivative of energy is probed with respect to number of electrons and the external potential while molecules approaching each other as follow: A good approximation to solve this expression is the use of "condensed" Fukui functions on an atom-by-atom basis: 84 where f k − and f k + are electrophilic and nucleophilic Fukui indices, respectively and q k is the atomic charge. Fukui indices for the B1, B2 and B3 molecules are listed in Table 9 according to the descending order of electrophilic Fukui function. For molecule B1, the highest ninth electrophilic atoms are those of benzimidazole six and ve-membered rings with Fukui indices between 0.101 and 0.023 then atoms N 14 (0.023), C 1 (0.019), C 2 (0.013), C 3 (0.009) and O 4 (0.005). Similar results were found for both B2 and B3 molecules and listed in Table 9 with the same manner. While these results match with those of NBOs and MEP map, Fukui indices are good estimation for the magnitude of interactions at specic atoms.  Table 10. From Fig. 16, it is obvious that the compounds B1, B2 and B3 adsorb to the surface of Fe (110) with a nearly at orientation. In accordance with the FMO, NBO and Fukui data, the heteroatoms (oxygen, sulfur, and nitrogen) lone pairs and p electrons either conjugated or isolated can transfer to the empty orbitals of the metallic substrate via strong coordination links. 85 The active sites distribution over the whole molecular skeleton of B1, B2 and B3 molecules guarantee maximum size adsorption and strong adherent protection layer formation that protect against corrosion. 86 At different modes of calculations (gas or aqueous), B1, B2 and B3 molecules obtained high negative values of adsorption energies to reveal a spontaneous favored adsorption. The values of binding energies enhanced for the protonated form to approach 380.794 kcal mol −1 for B3 molecule. The binding energies of B1, B2 and B3 molecules are greater than those of H 2 O molecules (in our calculation binding energies of water molecules ranged from 6.599 to 11.368), which supports the progressive replacement of H 2 O molecules from the surface of X56 c-steel. 87 These energy properties support the concept that the prevention of X56 c-steel corrosion was accomplished by the adsorption of the investigated molecules by the order B3 > B2 > B1.

Conclusions
Organic synthesis was conducted to obtain three new corrosion inhibitors to response to the vital and continues demand of carbon steel (X56) protection to alleviate the pressure on the petroleum industry as a result of the losses caused by metal corrosion. The synthesis included amino acids benzimidazole base derivatives that are expected to be a strong adsorbate to metal surface and at the same time cheap adhering lms. The conjugated system in the benzimidazole moieties besides the lone pairs of heteroatoms and the donating power of the methyl groups facilitate the adsorption to the metallic surface with priority of B3 due to the high donating power of S atom. The blocking of corrosion sites was conrmed by EFM, EIS and PDP electrochemical measurements. In addition, the EFM data were tted to six adsorption isotherms to validate the attachment to the metal surface. An overall inhibition efficiency of average 95-98% was obtained for both anodic and cathodic corrosion reactions through Langmuir adsorption of the inhibitor to X56 surface. SEM, in addition to FESEM, revealed an effective surface protection for inhibitor solutions rather than the blank one. DFT calculations conrmed a feasible and strong electron reallocation from the inhibitor HOMO to the metal surface.

Conflicts of interest
The authors declare that they have no known competing nancial interests or personal relationships that could have appeared to inuence the work reported in this paper.